Electromagnetic Induction Questions and Answers

Free Response Solve each problem showing all work Partial credit may be given kq 92 Nm FE c centi 10 m milli 10 3 micro 10 6 n nano 10 3 Q1 2 1 0 1 k 9 0x10 Q 2 3 4 5 6 Q3 7 8 b Find the magnitude of the force between Q1 and Q2 14 A positive charge Q 40 0 mC is located at a point X 2 00 m a positive charge Q2 30 0 mC is located at a point X2 3 00 m and a positive charge Q3 20 0 mC is located at a point X3 7 00 m a Draw free body diagrams for the electric force acting on Q Q2 and Q3 c Find the magnitude of the force between Q1 and Q3 9 d Find the magnitude of the force between Q2 and Q3 X m

Figure shows three conducting rails connected with resistances R R and 2R here R 59 A wire in form of sin curve x 2 sin y is being moved with constant velocity V 6 m s towards x axis A uniform magnetic field B 5 0 T is applied perpendicular to the plane of rails and wire Find out the current induced in 2R resistance Here x y both are in metres y V V R wwww wwww 2R X 16 ampere then find x

The magnetic flux through a coil varies with time t as shown in the diagram Which graph best represents the variation of the e m f E induced in the coil with time t pr 1 EA t 2 E q t

A toroid having 500 turns cross section 20cm and mean radius 40 cm is filled with medium H 350 Its self inductance is iw 1 87 5 mHboole Joulai 3 175 mH 2 44 mH bait 4 None Ag

In the adjacent figure the mutual inductance of the infinite straight wire and the coil is M while the self inductance of the coil is L The current in infinite wire is varying according to the relation 1 at where a is a constant and t is the time The time dependence of current in the coil is Ma A R Mit C 1 e R L MaL RI L R D none of the above B

2 In the adjacent figure the mutual inductance of the infinite straight wire and the coil is M while the self inductance of the coil is L The current in infinite wire is I varying according to the relation 1 at where a is a constant and t is the time The time dependence of current in the coil is Ma A R Mit C 1 e R MaL Rt L e R D none of the above B R

5 The magnetic flux through a stationary loop with resistance R varies during interval of time T as at Tt The heat generated during this time neglecting the inductance of loop will be 1 3 a T 3R a T 3R 2 4 a T 3R a T 3R

6 Consider a toroid of circular cross section of radius b major radius R much greater than minor radius b Find the total energy stored in toroid I is current a HN 126 2R c H N 1 6 b HoN 1 6 3R HN 126 d

A flat coil with a large number N of tightly wound turns in a uniform magnetic field perpendicular to the plane of the coil as shown in the figure The external radius of the coil is equal to a The magnetic field varies with time according to the law B Bo sin oot The maximum value of emf induced in the coil is Find the value of k NB k

A cylindrical region of radius 1 m has instantaneous homogeneous magnetic field of 5T and it is increasing at a rate of 2T s A regular hexagonal loop ABCDEFA of side 1 m is being drawn in to the region with a constant speed of 1 m s as shown in the figure What is the magnitude of emf developed in the loop just after the shown instant when the corner A of the hexagon is coinciding with the centre of the circle A 5 3 V C 5 3 2 V B 2 3 V D 5 3 n V D C E B 1 m xxxx xxx X Ax1 m s x x xxxx xx 1m x F Xxxxxx X X

current flows from straight wire as shown in figure and it is decreasing with time The induced current in loop placed near to it A In clockwise direction B In anticlockwise direction C Will not be produced B

The circuit NOR Is equivalent to 1 OR gate 3 AND gate NAND AB Aar NOT 2 NOR gate 4 NAND gate 13

A transformer is used to light a 100W and 110V lamp from a 220V mains If the main current is 0 5A the efficiency of the transformer is approximately 1 30 2 50 4 10

Two identical coaxial circular loops carry a current i each circulating in the same direction If the loops approach each other 1 the current in each loop will decrease 2 the current in each loop will increase 3 the current in each loop will remain the same 4 the current in one loop will increase and in the other loop will decrease

14 Two inductors L and L are connected in parallel and a time varying current flows as shown The ratio of currents i i2 at any time t is 12 1 L L 3 L L L L 1000001 00000 L 2 L L 4 L L L

15 In a coil of resistance of 10 92 the induced current developed by changing magnetic flux through it is shown in figure as a function of time The magnitude of change in flux through the coil in Weber is i A 4 1 8 3 6 0 0 1 17 t s AIPMT Mains 2012 2 2 4 4

An e m f of 15 volts is applied in a circuit containin henry inductance and 10 resistance The ratio current at time t o and t 1 sec is e 5 1 e0 5 1 3 1 e 1 e e 1 2 4 e 1

3 An electron moves on a straight line path XX as shown below A coil ABCD is kept adjacent to the path of electron What will be the direction of induced current if any in the coil B X A C D Y a ABCD b ADCB c The current will reverse its direction as the electron goes past the coil

A conducting circular loop of radius a and resistance R is kept on a horizontal plane A vertical time varying magnetic field B 2t is switched on at time t 0 Then 1 power generated in the coil at any time t is constant 2 flow of charge per unit time from any section of the coil is constant 3 total charge passed through any section between 4 R time t 0 to t 2 is

U 2 10 T 1 m 50 m s 10 v 1mV Some magnetic flux is changed from a coil of resistance 10 22 As a result an induced current is developed in it which varies with time as shown in figure The magnitude of change in flux through the coil in webers is 1 2 i amp 2 4 0 1 t s 3 6 4 8

angular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below JEE Main 2015 A C B Z I B I y B D X B B Z Z y If there is a uniform magnetic field of 0 3 T in the positive z direction in which orientations the loop would be in i stable equilibrium and ii unstable equilibrium a A and B respectively b A and C respectively B and D respectively d B and C respectively 1

E Two parallel conducting rails are connected to a source of emf E and internal resistance r Another conducting rod of length having negligible resistance lies at rest and can slide without friction over the rails A uniform magnetic field B is applied perpendicular to the plane of the rails At t 0 the rod is pulled along the rails by applying a force F The velocity of the rod is observed to be v Vo cos ot then find the power in watt spent by the force over 1 cycle Given B 2 Tesla r 2 x 102 vo 2 ms l 2cm r B Rod F l

A uniform magnetic field is restricted within a region of radius r The magnetic field changes with time dB at a rate Loop 1 of radius R r encloses the dt region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure below Then the e m f generated is NEET Phase 2 2016 3 1 Zero in loop 1 and zero in loop 2 2 dB dt dB dt dB in loop 1 and and R 2 dB in loop 2 R in loop 1 and zero in loop 2 in loon 1 and zero in loc

3 1 2 In the circuits a S2 are closed at t 0 and are kept closed for a long time The variation of currents in the two circuits for t 0 are roughly shown by figures are schematic and not drawn to scale tr E E R if a E R if ERH HR H E it R S a a b t t b t b a a b L tr E b R S

gin the plane of paper with constant angular velocity about O then which of the following graphs shows the variation of induced current with time f The magnetic field is perpendicular to the plane of loop as shown in the figure B X X X X X X X X X X X X X X X X X X X X h 1 E DE M 3 2 4 21 2 00

The current flows from A to B as shown in the figure The direction of the 1 clockwise 2 anticlockwise 3 straight line 4 none of these A B

Consider the circuit shown in figure a Find the current through the battery a long time after the S is closed b Suppose the switch is opened at t 0 What is the time constant of the decay Find the current through the inductor after one time constant R ww R wwmm

10 A conducting wire frame is placed in magnetic field which is directed into the paper The magnetic field is increasing at a constant rate The directions of induced current in wires AB and CD are 1 B to A and D to C 2 A to B and C to D 3 A to B and D to C 4 B to A and C to D X A X X X B X X X X X X X Cx X X DX

the direction opposite to ting current A non conducting ring having a uniformly distributed negative charge is placed in the plane of smooth paper A uniformly decreasing inward magnetic field is passing through the ring Then 8 1 Ring will start rotating anticlockwise 2 Ring will start rotating clockwise 3 Ring will jump and becomes floating above the paper 4 No change will be observed in the position of ring

1 63 in the figure a long thin wire carrying a varying current i 1 sin mot lies at a distance y above one edge of a HoloWo Cosewt rectangular wire loop of length L and width W lying in the x z plane If induced in the loop Find the value of A B C Scanned with W Art En YC emfis

A wire loop is rotated in a uniform magnetic field about an axis perpendicular to the field such that an EMF is induced The direction of the current induced in the loop reverses once each 1 Quarter revolution 2 Half revolution 3 Full revolution 4 Two revolutions

If a charge particle is projected at angle 8 with direction of parallel Electric and magnetic field as shown in figure then path of particle will be q too B 1 Circular 2 Helical with constant pitch 3 Helical with increasing pitch 4 Helical with decreasing pitch

G As shown in the figure a magnet is moved with a fast speed towards a coil at rest Due to this induced e m f induced current and induced charge in the coil is E I and Q respectively If the speed of the magnet is doubled the incorrect statement is 1 E increases IN S mmmm 2 increases O increases

4 0 2x A conductor lies along the Z axis at 1 5 Z 15 m and carries a fixed current of 10 0 A in a direction as shown in figure for a field B 3 x 10 e a T the total power required to move the conductor at constant speed to x 2 0 m y 0 m in 5 x 10 s is assume parallel motion along the X axis AIIMS 2017 2 0 Z 1 5 17 1 5 B Y 7 W

A coil in the shape of square is placed in a variable magnetic field which varies at the rate of dB dt as shown in figure The magnitude of emf between points a and d along path abcd will be B e dB dt far

A non conducting ring of radius R having uniformly distributed charge Q starts rotating about x x axis passing through diameter with an angular acceleration as shown in the figure Another small conducting ring having radius a a R is kept fixed at the centre of bigger ring is such a way that axis xx is passing through its centre and perpendicular to its plane If the resistance of small ring is r 102 find the induced current in it in ampere 16x10 Given q C R 1 m a 0 1 m x 8 rad s Ho X ff D R

225 A conducting movable rod AB lies across the frictionless parallel conducting rails in a uniform magnetic field B whose magnitude at t 0 is B The rod AB is given velocity v right ward and it continues to move with same velocity through out the f motion The acceleration due to gravity is along negative z axis i e g 10m s k ma of d m Which of the following graphs will be the best representation of magnitude of magnetic f versus time A B B D B

of Two uncharged identical capacitors A and B capacitanc inductor of inductance L are arranged as shown in the adjacent figure At t 0 the switch S is closed while switch S remains open At time t to LC switch S 2 is closed while switch S is opened Read the above passage carefully and answer the following questions Question 12 E E B II S S2 After switch S is closed and S is opened the maximum value of current through the inductor is C A B E 2L

rectangular coil of single turn having area A rotates in a uniform magnetic field B with angular speed w about an axis perpendicular to the field If initially the plane of the coil is perpendicular to the field then the average induced emf when it has rotated through 90 is 1 3 BA TU BA 2 4 BA 2 2 BA

lamps and two coils is connected to a dc source figure consisting of three identical D The ohmic resistance of the coils is negligible After some time switch S is opened Select correct alternative s just afterward Botton disconnect S A f L C 0000 C oooo Thuge coils b D 74576 LO L B C 1 Brightness of L remains same 2 Brightness of L becomes 2 times in of L becomes 3 times 3 Brightness 4 Brightnes of I

A rod of mass m and resistance r is placed on fixed resistanceless smooth conducting rails closed by a resistance R and it is projected with an initial velocity u Find its velocity as a function of time t 0 O m r B

A conducting rod of length 2 is rotating with constant angular speed o about its perpendicular bisector A uniform magnetic field exists parallel to the axis of rotation The emf induced between two ends of the rod is B Y 0

259 A square shaped wire frame carries a current i The edge of the frame is L The magnetic flux through the infinite region to the left of line AB is A 1 10 B Lin 4 a Hoi 2 Hoi a 2 Ho L In 1 1 L 2 2 H iL 4 2 a

36 A transformer has 500 primary turns and 10 secondary turns If the secondary has resistive load of 15 22 the currents in the primary and secondary respectively are 1 0 16 A 3 2 10 A 2 3 2 10 3 A 0 16 A 3 0 16 A 0 16 A 10 3 A

Two inductor coils of self inductance L 10 H and L 20 H are placed as shown in the figure The mutual inductance of the coil is 3 H The equivalent inductance between AB of the system of coils is 1 36 H 3 20H A oooooo B oooooo 2 24 H 4 38 H

An ideal DC source of emf E is an uncharged capacitor and inductor If switch is closed at t 0 what is the maximum charge om the capacitor in subsequent flow of charge 2 tell hat max e come S L moo C HH

A conducting square frame of side a and a long straight wire carrying current are located in the same plane as shown in the figure The frame moves to the right with a constant velocity V The emf induced in the frame will be proportional to 1 3 X 1 2x a 2x a 1 2x 2 2 4 1 V 1 AIPMT 2015

A dip needle is in the plane of magnetic meridian shows 30 Now it is rotated by an angle 30 then new dip angle will be tan 3 tan 3IN 2 tan 4 tan 1 2 3 3

15 If given arrangement is moving towards left with speed v then potential difference between B and D and current in the loop are respectively X X X B 1 BvR and non zero 21 ABVP and non zero X VE X X X X X B A 2R R C X X X 2 2BvR and zero 4 4BvR and zero dd Dwith constar

32 A particle of charge q mass m moving with velocity vo 1 enters a region of uniform magnetic field B Find displacement of particle for any arbitrary time t 1 Voti mvo qB 3 Voti mvo qB kash Educati qBt COS m COS qBt m 9 mvo qB mvo qB 1 sin sin qBt m k 2 2 mV 1 qB qBt 9 1 k m 2 Voti 4 Voti mvo qB mvo qB sin sin qBt m qBt m mvo qB mvo aB 1 cos COS qBt qBt